Hmmm. So the tyres are connected? If they were made seperately, then subdivided, then just 'slipped' onto the rims? Poly count would not be that much higher, maybe?

Another possibility is, if you made these tyres originally 'cut' from a sphere, then you could up the smoothness at the beginning when first dragging out the sphere and setting the divisions. (parametric?, yellow bounding box) Sorry to harp on, but good tyres are important on a bike...